'War brides', LAC says, are defined as "foreign civilian women who married Canadian soldiers serving overseas during the First and Second World Wars."

By? ( the Canadian military?) There is no doubt most of these women were British, so not 'foreign', but British subjects same as most women born in Canada. (And by the way, LAC, during WW I, Irish women were also British.)

And not all were civilians either. Possibly the assistance offered to civilian women, and dependants, if applicable, was not the same as extended to military women and not reflected in most of LAC's record collections. However if yours was a military bride, don't let LAC deter you, as for example, one of the record sets listed is 'Arrival of CWAC from overseas. Arrangements on Debarkation, 1943-1945'. CWAC stands for Canadian Women's Army Corps (WWII).

And I think there must have been at least a few brides other than overseas ones (and a few grooms). And LAC does make just a brief reference to women leaving Canada with or to join new husbands. "Library and Archives Canada also holds departure records for Canadian women who married servicemen from other Allied nations." I would think that USA/Canada Border records or other United States records may reference 'war marriages' either in the USA or Canada involving Canadians marrying USians too.

Not all war marriages may have been treated equally, depending on the status of the bride or groom. LAC lists '​Immigration; admission of fiancées of citizens of Chinese origin; enlargement of quota for India, 1956'.

In some cases, likely sad ones, LAC files may provide information on women and families after their arrival in Canada, for instance, in these files 'Assistance to dependents re desertion, bigamy, illegitimacy, 1940-47'. And passenger records will show some brides either leaving Canada later or visiting 'home' later on.
My own parents' marriage was a 'war marriage'. Both were British subjects and born in Canada. Both were in the Canadian military; they met and married in the United States. LAC does, I know, have records noting their marriage. Be sure to look at the entire file for your military person, if possible. This will be easier for Canadian WW I military once the files are all digitized and on-line, but seeing a WW II file may involve a longer process. And, in some cases, when a military person did not marry, but had, or was deemed responsible for, a child, there may well be information in the military files.
Don't neglect newspapers in your search. You will find articles about marriages and arrivals - even photos - as these marriages were of wide interest. Reading Library and Archives Canada's files may give you dates of marriage or arrivals, etc. to search by, or you may be lucky and find that a relevant newspaper has been indexed or even digitized and on-line.